Black hole mass and angular momentum in 2+1 gravity

TL;DR

This paper introduces a new, consistent way to define and compute the mass and angular momentum of black holes in 2+1 gravity, aligning with thermodynamic laws and applicable to various models.

Contribution

It proposes a novel, conserved quantity framework for black hole parameters in 2+1 gravity, ensuring consistency with thermodynamics and boundary conditions.

Findings

New definitions match quasilocal quantities

Framework satisfies Smarr-like formula

Results consistent with black hole thermodynamics

Abstract

We propose a new definition for the mass and angular momentum of neutral or electrically charged black holes in 2+1 gravity with two Killing vectors. These finite conserved quantities, associated with the SL(2,R) invariance of the reduced mechanical system, are shown to be identical to the quasilocal conserved quantities for an improved gravitational action corresponding to mixed boundary conditions. They obey a general Smarr-like formula and, in all cases investigated, are consistent with the first law of black hole thermodynamics. Our framework is applied to the computation of the mass and angular momentum of black hole solutions to several field-theoretical models.